The effect of damköhler number on the stand-off distance of cross-flow flames

Abstract

Cross-flow flames, formed between two reactants approaching at 90°, have many similarities to edge flames formed between parallel-flowing reactants. Two types can be distinguished: one whose inlet velocity profiles have a uniform strain rate and another whose inlet velocity profile is flat. Dimensional analysis suggests that the distance between the flame head and the confluence point, L _c , is affected by a Damköhler number. A simplified solution for the relationship between the non-dimensional stand-off distance Π and the Damköhler number is determined here by correlating the results of several hundred numerical simulations. For a cross-flow flame that is controlled by the strain rate, it is found that L _c ∝A𝒟^1/2τ_c ^1/2, where A is the strain rate, 𝒟 is the diffusivity and τ _c is the chemical time. For a convection-controlled flame, the expression is: L _c ∝U ³ τ _c ²𝒟⁻¹, where U is the entry velocity.